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Bohinc U.,Slovenian National Building And Civil Engineering Institute | Brank B.,University of Ljubljana | Ibrahimbegovics A.,CNRS Cachan Laboratory of mechanics and technology
Computer Methods in Applied Mechanics and Engineering | Year: 2014

We provide in this work the discretization error estimates that can guide an adaptive mesh refinement for the Discrete Kirchhoff plate finite elements. The proposed developments are built upon the concept of error estimates for classical elasticity and adapted to suit the Kirchhoff plate finite elements. We give a detailed illustration of the proposed procedures for the Discrete Kirchhoff triangular plate element, along with several different possibilities for constructing the enhancement of test space needed for error estimates. The first novelty concerns the consistent displacement field in terms of the third order polynomial for the Discrete Kirchhoff triangle, whereas the second novelty is the use of the Argyris triangle with fifth order polynomials for constructing the enhanced test for error estimates. We compare the latter against several alternatives that can be used for Kirchhoff plates. The results of numerical examples are given to illustrate the effectiveness of proposed discretization error estimates. © 2013 Elsevier B.V.

Choukairy K.,University Hassan 1 | Bennacer R.,CNRS Cachan Laboratory of mechanics and technology
Fluid Dynamics and Materials Processing | Year: 2012

This study carries the natural thermosolutal convection induced in heterogeneous porous media. The configuration considered is cartesian. The horizontal and vertical walls are submitted to different mass and heat transfer. The equations which govern this type of flow are solved numerically by using the finite volume method. The flow is considered two-dimensional and laminar. The model of Darcy and the approximation of the Boussinesq are taken into account. The parametr which control the problem are the thermal Darcy-Rayleigh number, Rt, the buoyancy ratio, N, the Lewis number, Le, the aspect ratio of the enclosure, A and the local permeability ratio, K r The flow fields, temperature and concentration are given for various values of the local permeability. The effects of increasing the local permeability, the thermal Darcy-Rayleigh number Rt and buoyancy ratio, N on the heat and mass transfer are discussed. These numerical results were confirmed analytically by using the parallel flow approximation. A good agreement was found between the two analytical and numerical approaches, which confirm the validity of the analytical approach in such heterogeneous domain. The flow intensity and transfer increase with the increase of the permeable heterogeneity of the domain. © 2012 Tech Science Press.

Hild F.,CNRS Cachan Laboratory of mechanics and technology
Mechanics of Materials | Year: 2015

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass, and rocks, or ductile materials such as steels and alloys. The main mechanism used herein to explain the change of the number of fragments with strain and stress rates is an obscuration (or shielding) phenomenon associated with cracking or cavitation. A probabilistic framework, which is based upon a Poisson point process, is introduced. Nonlocal (in space and time) expressions are obtained to account for multiple crack initiations or void nucleations, and their subsequent growth. This approach allows characteristic parameters (i.e. size, stress, stress rate, and time) involved in the fragmentation processes to be introduced. Examples are discussed to illustrate the use of these characteristic parameters in the analysis of dynamic fragmentation of brittle materials and spallation of tantalum. © 2014 Elsevier Ltd. All rights reserved.

This paper presents an analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its orientation with respect to the inflow in the far field is determined by the dip angle θ. As an application, we investigate the flow focusing effect for varying eccentricity ratios and dip angles. © 2010 International Association for Mathematical Geosciences.

Lubineau G.,CNRS Cachan Laboratory of mechanics and technology
International Journal of Damage Mechanics | Year: 2010

Modern approaches to the modeling of composites are no longer limited to the use of a single approach for the whole structure or for all the degradation mechanisms. On the contrary, modern advances enable the definition of truly multiscale models in order to describe the degradation. Thus, homogenized models can be rigorously deduced from the underlying micromechanics. In the past few years, LMT-Cachan has made a number of contributions to the three key points of these multiscale approaches: (1) the improvement of the reference model on the fine scale, (2) the definition of a controlled correspondence between the scales, and (3) the definition of the associated homogenized model. Here, the complete approach is formalized as a modeling pyramid. Each mechanism of degradation is described on the more relevant scale within an "hybrid micromechanical model". Based on the reference modeling, constitutive laws can be transfered within the unique framework of damage mechanics for being applied within commercial softwares. As an illustration, we focus more specifically on the homogenized law obtained for transverse cracking. The constitutive law and the material parameters issued from the homogenization, which define the model on the higher scale, are reviewed. Their identification is studied in detail. An important key point of the pyramidal approach appears here. Since it allows the interpretation of every quantity on different scales (both at the micromechanical and at the mesomechanical scales), the most relevant scale can be used for the identification of a chosen property. We limit ourselves to a "classical" identification. We mean by classical identification a procedure based on straight specimens. This process, to a certain extent, uses a parametric simulation of the nonlinear model based on a finite element representation of the test samples. The complete model is then used for the simulation of an industrial sample with hole. That example emphasizes the interest of underlying micromechanial variables for experimental validation. © The Author(s), 2010.

Panetier J.,CNRS Cachan Laboratory of mechanics and technology | Ladeveze P.,CNRS Cachan Laboratory of mechanics and technology | Ladeveze P.,Airbus | Chamoin L.,CNRS Cachan Laboratory of mechanics and technology
International Journal for Numerical Methods in Engineering | Year: 2010

In this work, we analyze a method that leads to strict and high-quality local error bounds in the context of fracture mechanics. We investigate in particular the capability of this method to evaluate the discretization error for quantities of interest computed using the extended finite element method (XFEM). The goal-oriented error estimation method we are focusing on uses the concept of constitutive relation error along with classical extraction techniques. The main innovation in this paper resides in the methodology employed to construct admissible fields in the XFEM framework, which involves enrichments with singular and level set basis functions. We show that this construction can be performed through a generalization of the classical procedure used for the standard finite element method. Thus, the resulting goal-oriented error estimation method leads to relevant and very accurate information on quantities of interest that are specific to fracture mechanics, such as mixed-mode stress intensity factors. The technical aspects and the effectiveness of the method are illustrated through two-dimensional numerical examples. © 2009 John Wiley & Sons, Ltd.

Gant F.,CNRS Cachan Laboratory of mechanics and technology | Rouch Ph.,Laboratoire Of Biomecanique | Louf F.,CNRS Cachan Laboratory of mechanics and technology | Champaney L.,CNRS Cachan Laboratory of mechanics and technology
International Journal of Solids and Structures | Year: 2011

The objective of this work is to define a simple linear model of joints used in aeronautics and to update this model efficiently. Industrial designers usually resort to semi-empirical linear joint models to represent the behavior of the joints of a large aeronautical structure. Here, we propose to develop a one-dimensional linear joint model which is capable of representing the behavior of every joint of a large structure globally while enabling local nonlinear reanalysis of the most highly loaded joints. Work on nonlinear reanalysis is not considered in this paper. In order to solve the numerical difficulties encountered in some of modeling situations, an updating strategy based on the constitutive relation error is proposed. Since the updating efficiency is significantly affected by the ratios of the stiffnesses of the different parts of the model, the strategy consists in rigidifying some parts of the model in order to control the updating accuracy and the rate of convergence. The numerical results of a standard model and a rigidified model illustrate the updating improvements allowed by the strategy. © 2010 Elsevier Ltd. All rights reserved.

Ngo M.,CNRS Cachan Laboratory of mechanics and technology | Ibrahimbegovic A.,CNRS Cachan Laboratory of mechanics and technology | Brancherie D.,CNRS Roberval Laboratory (Mechanical Research Unit)
Engineering Structures | Year: 2013

In this article we introduce a thermo-mechanical damage model, which is capable of representing the behavior of quasi-brittle materials subjected simultaneously to mechanical loading and heat transfer. Special care is taken of the quasi-brittle material behavior which can be represented by the continuum damage model, along with the solution procedures for fully coupled thermo mechanical loading conditions. © 2012.

Gant F.,CNRS Cachan Laboratory of mechanics and technology | Rouch Ph.,Laboratoire Of Biomecanique | Champaney L.,Arts et Metiers ParisTech
Computers and Structures | Year: 2013

The objective of this work is to develop a modeling strategy for assemblies involving multiple joints in an aeronautical predesign context. In the process of designing large structures, industrial engineers usually get around computational limitations by using submodeling techniques. When dealing with uncertain parameters, additional numerical difficulties appear due to the increase in the problem's size. In order to consider phenomena which vary during the global representation of the submodeling process, we propose a modeling approach for the scattering of these phenomena based on the Lack-Of-Knowledge theory. The proposed strategy is illustrated by the case of a multiple-joint assembly. © 2013 Elsevier Ltd. All rights reserved.

Ngo V.-M.,CNRS Cachan Laboratory of mechanics and technology | Ibrahimbegovic A.,CNRS Cachan Laboratory of mechanics and technology | Brancherie D.,CNRS Roberval Laboratory (Mechanical Research Unit)
Computers and Structures | Year: 2013

In this paper we present thermo-plasticity model for dealing with localized failure with softening, which is capable of accounting for mechanical loading and heat transfer simultaneously. The main point concerns the localized failure of the structure which results with heterogeneity of stress and strain field for temperature dependent properties. We discuss how to employ structured mesh for such case, and construct the appropriate enhancements of the displacement and temperature fields by using the finite element method with embedded discontinuities (ED-FEM). For clarity, we first consider 1D case, and provide several illustrative numerical simulations. We then provide the corresponding generalization of the proposed model to 2D case and its numerical implementation based upon structured ED-FEM mesh. © 2012 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

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